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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Lunar Distance in Wikipedia
From: George Huxtable
Date: 2007 Aug 2, 11:53 +0100
From: George Huxtable
Date: 2007 Aug 2, 11:53 +0100
Renee wrote- | | http://en.wikipedia.org/wiki/Lunar_distance_%28navigation%29 | I have made a major rewrite, partly from Paul's suggestions, partly from the | not-half-bad summary of lunars in the article on Celestial Navigation | (http://en.wikipedia.org/wiki/Celestial_navigation#Lunar_distance), and | partly from my own ideas. Sorry about that last part. I don't know when | the Nautical Almanac added the planets to the lunar distance tables, but I | am certain George can get back to us after he completes his article for | "Navigation News". | | I struck out the "Theory" section and subsumed the "practice" section into | the "Method" introductory paragraph. | I think Wikipedia now has the bare bones of a decent article. | We can leave it as-is and suggest further outside-of-wikipedia reading on | the subject (web pages AND books). | Or we can add as much information as all of you lunar experts can supply. | Explain the size of the error introduced if parallax is not corrected for. | Define "clearing". Describe (in 100 words or less) the difference between | the method of lunar distance, as originally presented by Maskeleyne, and the | "new lunars" recently discussed on this list. Fill in useful bits of | history (cross-reference the longitude article whenever possible). Add | citations (just place them in-line -- citation experts will rush in to turn | them into footnotes). If you how an encyclopedia article is supposed to | turn out, you get the gist of the style guidelines. Just typing in some | text is easy. You don't even have to create an account. ========================= Renee has tempted me to take a look at the revamped article. And indeed, it's a lot better. Still, there are one or two suggestions to offer, some errors to fix, additions to make. I wonder if Renee is prepared to have another go, rather than having several of us poking fingers into the pie. I will append a few suggested alterations, for Renee and others to shoot down or tinker with as they see fit. All the suggestions below are rather tentative. ========================= Lunar distance (navigation) From Wikipedia, the free encyclopedia In celestial navigation, lunar distance is the angle between the Moon and another celestial body. A navigator can use a lunar distance (also called a lunar) and a nautical almanac to calculate Greenwich time. The navigator can then determine longitude without a chronometer. =====That's good, I think. Nice and concise. [edit] Why Measure Lunar Distances? In Celestial navigation, precise knowledge of the time at Greenwich and the positions of one or more celestial objects are combined with careful observations to calculate latitude and longitude. [1] But accurate Greenwich time from chronometers was not generally available at sea until well into the 19th century. [2] [3] For nearly one hundred years (from about 1767 until 1850), the method of lunar distances was used to determine longitude at the time of the lunar observation. If a chronometer is available, longitude information can also be used to check and correct chronometer error.[2] =====Well, the last sentence is misleading. To correct a chronometer, you don't need longitude (which would call for an observation for local time). Just Greenwich Time, directly from the lunar, is all that's needed. And that shows up the problem with the previous sentence, because the lunar distance determines Greenwich Time, not longitude. It's just one step in determining longitude; but a major step. The next step is determining the local time. Only then do you have longitude. So my suggestion is to change the last two sentences into something like- "For nearly one hundred years (from about 1767 until 1850), mariners lacking a chronometer would use the method of lunar distances to determine Greenwich Time, an important step in finding their longitude. For those with a chronometer, its reading could be checked and corrected from a lunar determination of Greenwich Time [2]." Does that make sense? ===================== [edit] Method The method relies on the relatively quick movement of the moon across the background sky. It completes a circuit of 360 degrees in 27.3 days, about 1/2 degree per hour,[1] approximately equal to the angular diameter of the moon. The navigator precisely measures the angle between the moon and a body like the sun or a selected group of stars lying along the ecliptic. At that moment in time, anyone on the surface of the earth who can see the moon, would observe the same angle (corrected for errors). Certain almanacs list lunar distances in tables. The navigator can find the angle he or she measured, and thus know the time at Greenwich. Knowing Greenwich time and local time, the navigator can work out longitude. =======Can I suggest some changes here, for Renee to consider? Try this- Method. The method relies on the relatively quick movement of the Moon across the background sky, completing a circuit of 360 degrees in 27.3 days. In an hour, then, it will move about half a degree [1], roughly its own diameter, with respect to the background stars, and the Sun. Using a sextant, the navigator precisely measures the angle, slantwise across the sky, between the Moon and another body. That could be the Sun or one of a selected group of bright stars lying near the ecliptic, close to the Moon's path. At that same moment, anyone on the surface of the Earth, who could see those same two bodies, would observe the same angle between them (after important corrections had been made, as described below). Until the early years of the 20th century, almanacs listed predicted lunar distances to those bodies in tables, in relation to Greenwich Time. By comparing his corrected lunar distance with such a table, the mariner obtained the Greenwich Time of that observation. Local time was usually determined by a sextant observation of the altitude of the Sun [4] above the horizon [1], at morning or evening ; a star, rising or falling, could also be used. Then, longitude (from Greenwich) was readily calculated from the difference between local time and Greenwich Time, at 15 degrees per hour. =========Above, I've left those numbered citations in, without being sure how relevant they are to the text, without having those editions to hand to correspond with those page numbers. Would it be better to cross-refer to other entries within Wikipedia, where they are relevant? ======================= I think the section below is an important one, and I have expanded it considerably. It's not really more than a first-draft, but what do others think? [edit] Errors and corrections. A lunar distance changes with time at a rate of roughly half a degree, or 30 arc-minutes, in an hour. An error of just one arc-minute, then, will give rise to an error of about 2 minutes in Greenwich Time. The Earth spins at 15 degrees per hour, so that would lead to an error of half a degree, or 30 arc-minutes, in the resulting longitude; near the Equator; that corresponds to 30 miles. So lunar distance can never be a precise way to determine longitude, but nevertheless, to a navigator approaching a continent from the ocean, even such a rough figure was of great value. Thirty minutes in longitude was the target set by the famous Longitude Prize, which was won in the end, not by the lunar method, but by Harrison with his chronometer. In the early days of lunars, predictions of the Moon's position were good only to half an arc-minute, so to obtain the required overall precision of one arc-minute, only half a minute could be allowed for errors in measuring the lunar distance, and in calculation, combined. The best sextants could indicate angle to one-sixth of a minute, but in practice at sea, actual errors were somewhat larger, good observers typically achieving overall accuracy within half a minute in favourable conditions. From the unstable deck of a small vessel, in bad weather, with the sextant elevated and tilted at an awkward angle to get both objects simultaneously in view in its small mirrors, and with much of the sky obscured by square sails, it became a severe test of a navigator's skill. Almanac tables predicted lunar distances between the centre of the Moon and the centre of the Sun, as would be seen by an imaginary observer placed at the centre of a transparent Earth. In an observation, the centre of the Moon can not be estimated with sufficient accuracy. Instead lunar distances were always measured to the sharply lit, outer edge ("limb") of the Moon, and an allowance then made, from the almanac, for the Moon's "semidiameter", for that day; and similarly for the Sun. That was the first step in the correction process. The second step, always referred to as "clearing" a lunar, was in allowing for the effects of parallax and atmospheric refraction on the observed lunar distance. These vary, depending on the altitudes of the two bodies. Parallax, which changes the apparent position in the sky depending on the perspective of just where it's seen from, is especially important for the Moon, because it is so close to the Earth. It can shift the Moon's position by up to a whole degree, and has to be corrected for with great precision. In most celestial observations, measuring up from the horizon, correction for these effects would be a simple addition or subtraction. Not so for a lunar, however, because of its skewed angle. Instead, additional measurements are made of altitudes of the two bodies, close to the same moment as that of the lunar distance, high accuracy not being needed for those altitudes, in themselves. Great precision was required in the resulting calculations, however, which called for five-figure log tables of trig functions. In some circumstances, that additional measurement of Sun or star altitude could also be used to derive local time, bypassing the need for a separate observation. ========================== I will leave it at that for now, to see what reactions follow. Some tinkering with the history section might be worthwhile, and may appeal to others. George. contact George Huxtable at george@huxtable.u-net.com or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To , send email to NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---